A geometric approach to the construction of scientific impact indices

Two broad classes of scientific impact indices are proposed and their properties - both theoretical and practical - are discussed. These new classes were obtained as a geometric generalization of the well-known tools applied in scientometric, like Hirsch's h-index, Woeginger's w-index and the Kosmulski's Maxprod. It is shown how to apply the suggested indices for estimation of the shape of the citation function or the total number of citations of an individual. Additionally, a new efficient and simple O(log n) algorithm for computing the h-index is given. © 2009 Akadémiai Kiadó, Budapest.